Polarization Independent Metamaterial Absorber with Anti-Reflection Coating Nanoarchitectonics for Visible and Infrared Window Applications

The visible and infrared wavelengths are the most frequently used electromagnetic (EM) waves in the frequency spectrum; able to penetrate the atmosphere and reach Earth’s surface. These wavelengths have attracted much attention in solar energy harvesting; thermography; and infrared imaging applications for the detection of electrical failures; faults; or thermal leakage hot spots and inspection of tapped live energized components. This paper presents a numerical analysis of a compact cubic cross-shaped four-layer metamaterial absorber (MA) structure by using a simple metal-dielectric-metal-dielectric configuration for wideband visible and infrared applications. The proposed MA achieved above 80% absorption in both visible and near-infrared regions of the spectrum from 350 to 1250 nm wavelength with an overall unit cell size of 0.57λ × 0.57λ × 0.59λ. The SiO2 based anti-reflection coating of sandwiched tungsten facilitates to achieve the wide high absorption bandwidth. The perceptible novelty of the proposed metamaterial is to achieve an average absorptivity of 95.3% for both visible and infrared wavelengths with a maximum absorptivity of 98% from 400 nm to 900 nm. Furthermore, the proposed structure provides polarization insensitivity with a higher oblique incidence angle tolerance up to 45°.


Introduction
Most of the energy from the sun arrives in the form of visible light and near-infrared electromagnetic radiation. The wavelengths measuring from 2 to 2.6 µm and 3 to 6 µm are also known as near-and mid-infrared Earth's Atmospheric Transparency Window (ATW) [1]. Over the last decade, ATW research has drawn the attention of researchers after the concept of a perfect metamaterial absorber (PMA) in the gigahertz (GHz) frequency range was published [2,3]. Metamaterial absorbers (MA) in ATW offer various potential applications such as enhanced performance of solar radiation to energy conversion [4][5][6], researchers employ a complex metal structure (gear-shape) of Fe. This structure can make the MA physically fragile. Moreover, Fe layer without any protective coating can cause oxidation. A silicon-based nanostructured polarization-insensitive broadband plasmonic absorber was studied in the article [40], which tolerates wide-incident angles for both TM and TE modes between 514 THz and 638 THz with 99.90% peak absorption. As common infrared absorbers, most earlier investigations have concentrated on multi-layered structures with alternating layers of metal and dielectric plates. This is performed in order to increase the absorption bandwidths. For example, to obtain absorption from 3000 to 5500 nm, [41] proposed an MA with 20 metal-dielectric layers. Despite the MA's extensive infrared light absorption, the construction approach relies on expensive multipole nanofabrication processes. Furthermore, most investigations reveal that the polarization angle and incidence angle vary during practical use. This renders optical and infrared MA design more challenging to develop.
In addition, a simple MDM (metal-dielectric-meta) structured MA was described for optical and infrared regions of the spectrum. The uniqueness of the proposed structure is in its use of a small-size MA unit cell for both visible and near-infrared wavelength regions of the spectrum. The obtained absorber was further enhanced by introducing AR protective coating. A top layer of SiO 2 acts as an anti-reflection protective coating that enhances the absorption performance and protects the Tu metal layer from oxidation. The average absorption over the optical and first infrared spectrum includes the range of 380-1250 nm reaching 95.3%. Moreover, the absorption of the developed MA is polarizationindependent with a significant incident angle stable up to 45 • . Further, a brief study of the electric field, magnetic field, and current density have been presented. The MA shows numerous excellent characteristics, including low cost, simple fabrication, simultaneous ultra-broad, and perfect absorption performances. Figure 1 depicts the unit cell design. The ultimate design of this cell contains four layers. The top layer is a SiO 2 anti-reflection (AR) coating, and the bottom metal layer is tungsten (Tu), which acts as a reflector. There are two layers of SiO 2 in between the AR and the reflective layer. One is the intermediate layer between the resonator and the ground, and the other is wrapped around the tungsten resonator. The final layer thicknesses are h1 = 105 nm, h2 = 12.5, h3 = 68, h4 = 21, respectively, resulting in a total thickness of 206.5 nm. The width of the proposed unit cell is W1 = 200 nm. Table 1 contains detailed structural information of MA. Simulation of the proposed MA unit cell was performed with CST Studio Suite [42]. Periodic boundary conditions have been applied for sidewall, where two floquet ports were applied at the top and bottom of the structure. Tungsten is substantially more dependable for a broad frequency band in the optical range and infrared range application than other commonly used metals in MA. At the same time, the use of tungsten can greatly reduce the production cost compared to the previous studies. For a typical sample of tungsten, the refractive index and excitation coefficient at 632.8 nm or mid optical window band are 3.63739 and 2.916877, respectively. On the other side of SiO 2 , the refractive index and excitation coefficient at 632.8 nm are 1.45704 and 0, respectively. Figure 2 shows the refractive index and excitation coefficient of tungsten and SiO 2 in the optical and infrared range.     Later in this paper, different metals and media are compared. As the bottom layer comprises tungsten, the transmission of light is prevented. Therefore, the formula for absorption is represented by Equation (1) [29].

Unit Cell Design
where A is absorption and R is reflectance. In Figure 2, the optical parameters of Tungsten (Tu), and SiO 2 are illustrated, obtained from [43][44][45]. For the vertical incident of electromagnetic wave, TM mode was used as the proceeding EM wave across the negative z-axis, and polarization of the proceeding light was aimed across the x-axis.

Result Analysis
The absorption of the proposed MA structure is illustrated in Figure 3. Over 90% absorption (nearly perfect absorption) was achieved by the MA in its targeted wavelengths. It achieved an average of 95.3% absorption throughout the wavelengths from 350 to 1250 nm. According to the simulated result, the proposed structure has a peak absorption of 98.2% at 602 nm wavelength. Later in this paper, different metals and media are compared. As the bottom layer comprises tungsten, the transmission of light is prevented. Therefore, the formula for absorption is represented by Equation (1) [29].
where A is absorption and R is reflectance. In Figure 2, the optical parameters of Tungsten (Tu), and SiO2 are illustrated, obtained from [43][44][45]. For the vertical incident of electromagnetic wave, TM mode was used as the proceeding EM wave across the negative zaxis, and polarization of the proceeding light was aimed across the x-axis.

Result Analysis
The absorption of the proposed MA structure is illustrated in Figure 3. Over 90% absorption (nearly perfect absorption) was achieved by the MA in its targeted wavelengths. It achieved an average of 95.3% absorption throughout the wavelengths from 350 to 1250 nm. According to the simulated result, the proposed structure has a peak absorption of 98.2% at 602 nm wavelength. Considering the practical applications, wide bandwidth and high absorption rate are useful indicators when designing an absorber. An absorber must be insensitive to the large incident angle and independent of polarization. The proposed design was simulated and then improved gradually. The materials of the resonating metal surface bear a key influence on the absorption characteristic of the MA, which can be tested by using different materials alternatively. In Figure 4, a comparative study of different metals has been better performed to understand the absorption characteristic of the metamaterial unit cell. Tungsten represents an attractive material for PMA design in the optical spectrum, whereas germanium (Ge), aluminium (Al), and iron show lower absorption. The difference in refraction index of these materials is the reason behind this variation. Gold (Au) shows almost perfect absorption at 400 nm, but after 450 nm, the absorption decreases rapidly. Copper (Cu) demonstrates almost the same absorption characteristics. Figure 4 shows the comparison of different resonating components. For visible and infrared spectrum MA, the absorption and extensiveness of the bandwidth are only slightly affected by the refractive index of the metal [46]. Figure 5 shows the refraction index of Tu, Ge, Al, and iron. Considering the practical applications, wide bandwidth and high absorption rate are useful indicators when designing an absorber. An absorber must be insensitive to the large incident angle and independent of polarization. The proposed design was simulated and then improved gradually. The materials of the resonating metal surface bear a key influence on the absorption characteristic of the MA, which can be tested by using different materials alternatively. In Figure 4, a comparative study of different metals has been better performed to understand the absorption characteristic of the metamaterial unit cell. Tungsten represents an attractive material for PMA design in the optical spectrum, whereas germanium (Ge), aluminium (Al), and iron show lower absorption. The difference in refraction index of these materials is the reason behind this variation. Gold (Au) shows almost perfect absorption at 400 nm, but after 450 nm, the absorption decreases rapidly. Copper (Cu) demonstrates almost the same absorption characteristics. Figure 4 shows the comparison of different resonating components. For visible and infrared spectrum MA, the absorption and extensiveness of the bandwidth are only slightly affected by the refractive index of the metal [46]. Figure 5 shows the refraction index of Tu, Ge, Al, and iron.   As with the materials, the MA's absorption is related to the number of la The proposed design is a four-layer MA. The absorption by different layer Figure 6. It can be seen that the increased number of layers also directly influ tion. However, the addition of more layers renders the design process com sult, there is a trade-off between layer count and absorption. In Figure 6, in c the other structures, the final structure can provide a broader absorption ban 350 nm to 1250 nm. More importantly, the final MA structure covers the opti   As with the materials, the MA's absorption is related to the numb The proposed design is a four-layer MA. The absorption by differen Figure 6. It can be seen that the increased number of layers also direct tion. However, the addition of more layers renders the design proces sult, there is a trade-off between layer count and absorption. In Figure the other structures, the final structure can provide a broader absorpti As with the materials, the MA's absorption is related to the number of layers [47][48][49]. The proposed design is a four-layer MA. The absorption by different layers is shown in Figure 6. It can be seen that the increased number of layers also directly influence absorption. However, the addition of more layers renders the design process complex. As a result, there is a trade-off between layer count and absorption. In Figure 6, in comparison to the other structures, the final structure can provide a broader absorption bandwidth from 350 nm to 1250 nm. More importantly, the final MA structure covers the optical and near-infrared spectrum with polarization-independent and angle insensitive behaviour. Figure 6 shows the evaluation of the structure. The structure initially had only two layers. A bottom tungsten layer with a thickness of 105 nm and a top silicon dioxide layer with a thickness of 12.5 nm. This initial structure has an average absorption of 50% from 380 nm to 900 nm wavelength. Then, a tungsten bar with a length of 157.20 nm and width of 31.5 nm was introduced on top of the SiO 2 layer. This new structure gave a 65% average absorption. Following this, another tungsten bar with the same length and width was placed on top of the SiO 2 layer. However, this bar is 90 • clockwise rotated, forming a cross-like shape. The structure now starts to show better absorption compared to the previous structures. It has almost 97% absorption at 380 nm wavelength and an average of 80% absorption for the rest wavelength. However, as this layer is a metal surface, it reflects some of the incident light. As a result, this structure cannot absorb as expected. To solve this problem, a layer of SiO 2 has been used to prevent reflection from the body of the metal cross. This gives a peak absorption of 95% from 400 nm to 800 nm. A layer of SiO 2 has been introduced in the final structure to prevent reflection from the top. As a result, 97% absorption from 400 nm to 900 nm was finally achieved. The effect of SiO 2 as an anti-reflection surface will be explained later on in this article.
aterials 2022, 15, x FOR PEER REVIEW It has almost 97% absorption at 380 nm wavelength and an average of 80% the rest wavelength. However, as this layer is a metal surface, it reflects so dent light. As a result, this structure cannot absorb as expected. To solve t layer of SiO2 has been used to prevent reflection from the body of the me gives a peak absorption of 95% from 400 nm to 800 nm. A layer of SiO2 h duced in the final structure to prevent reflection from the top. As a result, 9 from 400 nm to 900 nm was finally achieved. The effect of SiO2 as an anti-ref will be explained later on in this article. On the other hand, the cross shape is the key resonant element of the the thickness of the tungsten cross resonator. As a result, the absorption is its thickness Figure 8 shows as the thickness (h3) decreases from 68 nm to 3 tion bandwidth shrinks from 900 nm to 650 nm (from 350 nm-1250 nm to 35 in a periodic manner. In terms of peak absorption, it remains almost the sa Tungsten acts as a metal blocking layer at the bottom of the MA, preventing waves from propagating through it [50]. The blocking capability of EM waves can be understood by skin depth δ = ρ/π f µ = ρλ/πµ, where wavelength is proportional to skin depth. So, a higher skin depth is required to block the larger wavelength [17,51]. Figure 7 shows the investigation of absorption property for different back layer thicknesses from h1 = 105 to 65, where the absorption is reduced in the near-infrared region with the decrease of the thickness h1. This phenomenon occurs due to the increase in EM transmission. On the other hand, the cross shape is the key resonant element of the MA, and h3 is the thickness of the tungsten cross resonator. As a result, the absorption is influenced by its thickness Figure 8 shows as the thickness (h3) decreases from 68 nm to 34 nm, absorption bandwidth shrinks from 900 nm to 650 nm (from 350 nm-1250 nm to 350 nm-950 nm) in a periodic manner. In terms of peak absorption, it remains almost the same up to h3 = 45 nm. However, when h3 is near 34 nm, peak absorption decreases to 95% from 98%.  The cross shape is a key resonant element of the MA, and h3 is the thi tungsten cross resonator. As a result, the absorption is influenced by its thic Figure 9 shows the angular stability characteristics of the absorber. Her angle of oblique incidence. The simulated result shows that the absorber is st = 45°". Beyond this, the MA starts to lose its angular stability, and becomes u "θ = 75°". The reason behind this is the SiO2 coating. In Figure 10, it can be  The cross shape is a key resonant element of the MA, and h3 is the th tungsten cross resonator. As a result, the absorption is influenced by its thic Figure 9 shows the angular stability characteristics of the absorber. He angle of oblique incidence. The simulated result shows that the absorber is s = 45°". Beyond this, the MA starts to lose its angular stability, and becomes "θ = 75°". The reason behind this is the SiO2 coating. In Figure 10, it can be critical angle of reflection of SiO2 is from "55°" in the infrared optical spect The cross shape is a key resonant element of the MA, and h3 is the thickness of the tungsten cross resonator. As a result, the absorption is influenced by its thickness. Figure 9 shows the angular stability characteristics of the absorber. Here, θ (theta) is angle of oblique incidence. The simulated result shows that the absorber is stable up to "θ = 45 • ". Beyond this, the MA starts to lose its angular stability, and becomes unstable after "θ = 75 • ". The reason behind this is the SiO 2 coating. In Figure 10, it can be seen that the critical angle of reflection of SiO 2 is from "55 • " in the infrared optical spectrum [36]. As a result, the incident light starts to reflect in the incident medium causing the MA to lose its absorption capacity. As a result, the MA becomes angular-unstable after "θ = 55 • ". This represents a research opportunity for future studies.   Figure 11 illustrates the polarization independency of the proposed MA. It can be seen that the MA is polarization independent for the range "phi = 0°" to "phi = 90°". There is a little change in absorption curve from "phi = 75°" to "phi = 90°". However, it does not affect the overall absorption bandwidth of the MA.   Figure 11 illustrates the polarization independency of the proposed seen that the MA is polarization independent for the range "phi = 0°" to "ph is a little change in absorption curve from "phi = 75°" to "phi = 90°". Howev affect the overall absorption bandwidth of the MA.  Figure 11 illustrates the polarization independency of the proposed MA. It can be seen that the MA is polarization independent for the range "phi = 0 • " to "phi = 90 • ". There is a little change in absorption curve from "phi = 75 • " to "phi = 90 • ". However, it does not affect the overall absorption bandwidth of the MA. To demonstrate the anti-reflection effect of SiO2, the absorption spectrum of the MA was examined in three different component setups. Figure 12a illustrates the average absorption of three-component setups. It can be seen that the structure without any antireflection layer has the lowest average absorption of 88%. At the same time, the structure with a partial anti-reflection layer bears a comparatively better average absorption of 90% However, the greatest average absorption of 93% was achieved by the structure with a complete SiO2 anti-reflection layer. Figure 12b illustrates the overall absorption of threecomponent setups with their corresponding structures. A comparison of SiO2 at various thicknesses is shown in Figure 13. It is clear that the thickness of the SiO2 has an impact on the MA's absorption capacity. The absorption bandwidth increases with increases in SiO2 thickness, while average peak absorption falls. If the thickness decreases, the opposite occurs. A thin SiO2 layer was employed in the fina design of this study to keep the unit cell size to a minimum. To demonstrate the anti-reflection effect of SiO 2 , the absorption spectrum of the MA was examined in three different component setups. Figure 12a illustrates the average absorption of three-component setups. It can be seen that the structure without any antireflection layer has the lowest average absorption of 88%. At the same time, the structure with a partial anti-reflection layer bears a comparatively better average absorption of 90%. However, the greatest average absorption of 93% was achieved by the structure with a complete SiO 2 anti-reflection layer. Figure 12b illustrates the overall absorption of three-component setups with their corresponding structures. To demonstrate the anti-reflection effect of SiO2, the absorption spectrum of the MA was examined in three different component setups. Figure 12a illustrates the average absorption of three-component setups. It can be seen that the structure without any antireflection layer has the lowest average absorption of 88%. At the same time, the structure with a partial anti-reflection layer bears a comparatively better average absorption of 90%. However, the greatest average absorption of 93% was achieved by the structure with a complete SiO2 anti-reflection layer. Figure 12b illustrates the overall absorption of threecomponent setups with their corresponding structures. A comparison of SiO2 at various thicknesses is shown in Figure 13. It is clear that the thickness of the SiO2 has an impact on the MA's absorption capacity. The absorption bandwidth increases with increases in SiO2 thickness, while average peak absorption falls. If the thickness decreases, the opposite occurs. A thin SiO2 layer was employed in the final design of this study to keep the unit cell size to a minimum. A comparison of SiO 2 at various thicknesses is shown in Figure 13. It is clear that the thickness of the SiO 2 has an impact on the MA's absorption capacity. The absorption bandwidth increases with increases in SiO 2 thickness, while average peak absorption falls. If the thickness decreases, the opposite occurs. A thin SiO 2 layer was employed in the final design of this study to keep the unit cell size to a minimum. The electric and magnetic fields (EF and HF) are discussed below to understand the proposed MA's absorption mechanism better. Figures 14a-f and 15a-f show that the EM field is intensified at some regions of the MA peak absorption point wavelength. A dipolar field density has formed between the metal resonator and the metal bottom layer. It can be seen that EF and HF density formed perpendicularly in different structure positions for the same wavelength. HF is highly induced in the insulating layer due to resonance of the surface plasmons. The outer corners of the Tu-cross experience greater excitation than the middle. The cavity gap between the surrounding Tu crosses of other unit cells is one of the reasons behind this. The electric and magnetic fields (EF and HF) are discussed below to understand the proposed MA's absorption mechanism better. Figures 14a-f and 15a-f show that the EM field is intensified at some regions of the MA peak absorption point wavelength. A dipolar field density has formed between the metal resonator and the metal bottom layer. It can be seen that EF and HF density formed perpendicularly in different structure positions for the same wavelength. HF is highly induced in the insulating layer due to resonance of the surface plasmons. The outer corners of the Tu-cross experience greater excitation than the middle. The cavity gap between the surrounding Tu crosses of other unit cells is one of the reasons behind this. The electric and magnetic fields (EF and HF) are discussed below to understand the proposed MA's absorption mechanism better. Figures 14a-f and 15a-f show that the EM field is intensified at some regions of the MA peak absorption point wavelength. A dipolar field density has formed between the metal resonator and the metal bottom layer. It can be seen that EF and HF density formed perpendicularly in different structure positions for the same wavelength. HF is highly induced in the insulating layer due to resonance of the surface plasmons. The outer corners of the Tu-cross experience greater excitation than the middle. The cavity gap between the surrounding Tu crosses of other unit cells is one of the reasons behind this. As illustrated in Figures 16 and 17, the resonance mechanism is explored by comparing the surface current of the metal layer at 450 nm and 1150 nm wavelengths, respectively. At 450 nm, there is a large polarization rotation impact, but at 1150 nm, there is a negligible polarization rotation effect. The surface current is estimated using a linearly polarized incidence oriented on the x-axis, with red arrows indicating the current flow direction. As illustrated in Figures 16 and 17, the resonance mechanism is explored by comparing the surface current of the metal layer at 450 nm and 1150 nm wavelengths, respectively. At 450 nm, there is a large polarization rotation impact, but at 1150 nm, there is a negligible polarization rotation effect. The surface current is estimated using a linearly polarized incidence oriented on the x-axis, with red arrows indicating the current flow  Figures 16 and 17, the resonance mechanism is explored by comparing the surface current of the metal layer at 450 nm and 1150 nm wavelengths, respectively. At 450 nm, there is a large polarization rotation impact, but at 1150 nm, there is a negligible polarization rotation effect. The surface current is estimated using a linearly polarized incidence oriented on the x-axis, with red arrows indicating the current flow direction.   Table 2 shows the comparison between previous studies and the prese ture. It can be seen that the presented MA bears the most considerable ab width, and a relatively good average absorption spectrum while only usin cient constituents with a four-layer structure. This MA covers the optical and the near-infrared spectrum. Most remarkably, it bears the smallest siz MA structures.   Table 2 shows the comparison between previous studies and the pre ture. It can be seen that the presented MA bears the most considerable width, and a relatively good average absorption spectrum while only us cient constituents with a four-layer structure. This MA covers the optic and the near-infrared spectrum. Most remarkably, it bears the smallest MA structures.  Table 2 shows the comparison between previous studies and the presented MA structure. It can be seen that the presented MA bears the most considerable absorption bandwidth, and a relatively good average absorption spectrum while only using two costefficient constituents with a four-layer structure. This MA covers the optical range entirely and the near-infrared spectrum. Most remarkably, it bears the smallest size among other MA structures.

Conclusions
An optical and infrared window MA consisting of metal-dielectric with metal antireflection coating was theoretically obtained and studied. The proposed MA revealed an average absorption of 95.3% from 350 nm to 1250 nm wavelength, corresponding to the optical range and the near-infrared spectrum. Furthermore, the MA achieved complete polarization insensitivity and an angular stability up to 45 • . The physical properties of perfect broadband absorption were thoroughly investigated. The proposed MA with a simple structure shows a larger absorption band of 900 nm, peak absorption of 98%, and the smallest size of 0.57λ × 0.57λ × 0.59λ. These properties render the proposed MA suitable for optical and infrared window applications. Moreover, this study provides guidelines for future ATW research.

Data Availability Statement:
The data presented in this study are presented in this article.